Subgroups — C₇×#395 #90041

Order 448.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₄⋊C₄	C₂	1	3	yes	maximal
3	C₇×#95	C₂	1	3	yes	maximal
4	C₂×C₇×Q₈	—	2	6	no	—
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₇	C₂²	1	3	yes	—
7	C₂²×C₄×C₇	C₂²	1	3	yes	—
8	C₇×C₄⋊C₄	—	2	6	no	—
9	#395	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₇	C₂³	1	1	yes	characteristic
11	C₇×Q₈	—	2	8	no	—
12	C₂×C₄×C₇	—	2	3	no	—
13	C₂×C₄×C₇	—	2	6	no	—
14	C₂×C₄×C₇	—	2	3	no	—
15	C₂×C₄×C₇	—	2	3	no	—
16	C₂×C₄×C₇	D₄	1	6	yes	—
17	C₂×C₄×C₇	Q₈	1	6	yes	complemented
18	C₂²×Q₈	C₂×C₇	1	1	yes	characteristic
19	C₂×C₄⋊C₄	C₂×C₇	1	3	yes	—
20	#95	C₂×C₇	1	3	yes	—
21	C₂²×C₇	C₂×D₄	1	3	yes	—
22	C₂²×C₇	C₂×Q₈	1	3	yes	—
23	C₂²×C₇	#41	1	1	yes	characteristic
24	C₄×C₇	—	2	6	no	—
25	C₄×C₇	—	2	6	no	—
26	C₄×C₇	—	4	1	no	—
27	C₂×Q₈	—	2	6	no	—
28	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
29	C₂²×C₄	C₂²×C₇	1	3	yes	—
30	C₂²×C₄	C₂²×C₇	1	3	yes	—
31	C₄⋊C₄	—	2	6	no	—
32	C₂×C₇	#120	1	1	yes	characteristic
33	C₂×C₇	C₂²⋊Q₈	1	3	yes	—
34	C₂×C₇	C₄⋊Q₈	1	3	yes	—
35	C₂³	C₂³×C₇	1	1	yes	characteristic
36	Q₈	—	2	8	no	—
37	C₂×C₄	—	2	3	no	—
38	C₂×C₄	—	2	6	no	—
39	C₂×C₄	—	2	3	no	—
40	C₂×C₄	—	2	3	no	—
41	C₂×C₄	C₇×D₄	1	6	yes	—
42	C₂×C₄	C₇×Q₈	1	6	yes	complemented
43	C₇	#395	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₂×C₇×D₄	1	3	yes	—
45	C₂²	C₂×C₇×Q₈	1	3	yes	—
46	C₂²	C₇×#41	1	1	yes	characteristic
47	C₄	—	2	6	no	—
48	C₄	—	2	6	no	—
49	C₄	—	4	1	no	—
50	C₂	C₇×#120	1	1	yes	characteristic
51	C₂	C₇×C₂²⋊Q₈	1	3	yes	—
52	C₂	C₇×C₄⋊Q₈	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. #395	C₇	direct (N × H)
17. C₂×C₄×C₇	Q₈	semidirect
42. C₂×C₄	C₇×Q₈	semidirect
43. C₇	#395	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×Q₈	2
C₂×C₇×C₄⋊C₄	2
C₇×#95	2
#395	7

Subgroups — C7×#395 #90041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#395 #90041